


Paper Title:
Asymptotic Analysis of Positive Decreasing Solutions of a Class of Systems of Second Order Nonlinear Differential Equations in the Framework of Regular Variation
Author(s):
Jaroslav Jaroš, Kusano Takaŝi, Tomoyuki Tanigawa
Department of Mathematical Analysis and
Numerical Mathematics,
Faculty of Mathematics, Physics and Informatics,
Comenius Universiy, 842 48 Bratislava,
Slovakia.
Email: ksntksjm4@gmail.com
Professor Emeritus at: Hiroshima
University,
Department of Mathematics, Faculty of Science,
HigashiHiroshima 7398526,
Japan.
Email: jaros@fmph.uniba.sk
Department of Mathematics, Faculty of
Education,
Kumamoto University, Kumamoto 8608555,
Japan.
Email:
tanigawa@educ.kumamotou.ac.jp
Abstract:
The system of nonlinear differential equations
is under consideration, where α_{i}
and β_{i} are positive constants and
p_{i}(t) and q_{i}(t) are continuous regularly varying functions
on [a,∞). Two kinds of criteria are established for
the existence of strongly decreasing regularly varying solutions with negative
indices of (A) with precise asymptotic behavior at infinity. Fixed point
techniques and basic theory of regular variation are utilized for this purpose.
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